To the best of my understanding, no, and no, are the answers to your questions. Present believers will not go through any part of the 70th week (also known as the seven-year tribulation) and we will not know the antichrist before the rapture. I base this on three simple principles (instead of endless arguments over lengthy passages). Here they are:
- Present-day believers will be taken out of the world before the wrath of God is fully poured out on the earth. 1 Thessalonians 1:10 clearly teaches that Jesus has "delivered us from the wrath to come." I do not believe that hell is the wrath to come. That is the wrath or judgment to which men will go. The wrath to come points to the tribulation. Revelation 6:17 defines it as such, "For the great day of his wrath is come; and who shall be able to stand?" Some argue that this refers only to a part of the tribulation, but I disagree. But instead of arguing this, let us look at the next principle.
- Present-day believers are told to look for the coming of the Son of God for them and not for the signs of His coming. The last days for the grace age Christian are defined strictly in spiritual terms (see 1 Timothy 4:1-2; 2 Timothy 3:1-9). We are not told to look for the antichrist or for signs in the heaven or on earth beneath. Explicitly, we are told, "Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ" (Titus 2:13). We are to be "waiting for the coming of our Lord Jesus Christ" (1 Corinthians 1:7). "For our conversation is in heaven; from whence also we look for the Saviour, the Lord Jesus Christ" (Philippians 3:20). To me, this is a tremendous and important principle concerning the rapture and its timing. Any system that gets us looking for signs or for the antichrist is a system that is in error.
- The entirety of the seventy weeks of Daniel are said to be "determined upon thy people and upon thy holy city" (Daniel 9:24). God's people in context are clearly the Jewish people and the holy city is Jerusalem. I agree that the seventieth week of Daniel refers to the seven years of tribulation. The Bible says that this time is for the purpose of completing God's work with the Jewish people. I know that Revelation refers to multitudes being redeemed out of all nations, but that is a side issue. The seventieth week is for the Jewish people. It is not for the Gentile or Jewish believers of the age of grace. Why then should the believers of today go through any part of this week?
When taken together, I believe that these three principles make a very strong argument for the teaching that grace age believers will be raptured out of this world before the beginning of the seventieth week and before the revelation of the antichrist. I do not expect this would convince those who wish to spend their energies in arguing their particular take on prophecy, but that is not my purpose. I only hope that it is a help to some who are honestly looking for some biblical answers.